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Superluminal Signals and Causality

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Superluminal Signals and Causality Annales de la Fondation Louis de Broglie, Volume 28, no 3-4, 2003 507 Superluminal signals and causality F. SELLERI Università di Bari - Dipartimento di Fisica INFN - Sezione di Bari I 70126 Bari, Italy ABSTRACT. Transformations of space and time depending on a synchronisation parameter, e1, generalize the Lorentz transformations which ≠ are reobtained for a particular e1 0. No fundamental experiment of relativity depends on the choice of e1, but if accelerations are considered = only e1 0 remains possible. Electromagnetic superluminal signals (SLS) have recently been detected in several experiments. The causal paradoxes generated by SLS in the theory of relativity are shown to be naturally solved if the SLS propagate in a Lorentz ether at rest in a privileged inertial system S 0 . This conclusion is compatible with all the experimental evidence. 1. The inertial transformations of space and time In this first section previous results are reviewed which provide the basis of a sound theoretical treatment of superluminal signals (SLS). According to Poincaré [1], Reichenbach [2], Jammer [3] and Mansouri and Sexl [4] the clock synchronisation in inertial systems is conventional and the choice based on the invariance of the one way velocity of light made in the TSR was only based on simplicity. In [5] we showed that a suitable parameter e1 can be introduced to allow for different synchronisations in the transformations of the space and time variables. The TSR is obtained for a particular nonzero 508 F. Selleri = value of e1. It was also found, however, that the choice e1 0 is the only one allowing for a treatment of accelerations rationally connected with the physics of inertial systems. These results are reviewed in the present section. Given the inertial frames S0 and S one can set up Cartesian coordinates and make the following standard assumptions: (i) Space is homogeneous and isotropic and time homogeneous, at least if judged by observers at rest in S0 ; (ii) In the system S0 the velocity of light is " c " in all directions, so that clocks can be synchronised and one way velocities can be measured in S0 ; (iii) The origin of S, observed from S0 , is seen to move with velocity + v< c parallel to the x 0 axis, that is according to the equation = x 0 v t0 ; = = (iv) The axes of S and S0 coincide for t t0 0 ; The system S0 turns out to have a privileged status in all theories satisfying these assumptions, with the exception of the TSR. Two further assumptions based on direct experimental evidence can be added: (v) The two way velocity of light is the same in all directions and in all inertial systems [6]; (vi) Clock retardation takes place with the usual velocity dependent factor when clocks move with respect to S0 [7-10]. These conditions were shown [5] to imply for the transformations of the space and time variables from S0 to S; Superluminal signals and causality 509 − = x 0 v t 0 x R y = y ; z = z 0 0 (1.1) t = R t + e x − v t 0 1 0 0 where R = 1 − v 2 / c2 (1.2) Using (v) and eq.s (1.1), the one way velocity of light relative to the rmoving θ system S for light propagating at an angle from the velocity v of S relative to S0 is [11] : c c (θ) = (1.3) 1 1 + Γ cosθ with v Γ = + e R (1.4) c2 1 while, of course, the two way velocity of light relative to S is c in all directions. The inverse transformations of (1.1) are = − + v t x 0 (R e1v) x R = = y 0 y ; z0 z (1.5) t − R e x t = 1 0 R Theories with different e1‘s imply the existence of a privileged inertial system, S0 . Thus, if one such theory describes correctly the physical reality a particular inertial system has to exist in which time is truly physical. This should be the system in which the Lorentz ether is at rest. The TSR is a particular case given by 510 F. Selleri = − v e1 2 (1.6) c R Γ = θ = giving 0 and c1( ) c and reducing (1.1) and (1.5) to their Lorentz form. The transformations (1.1) in differential form are − = d x 0 v d t 0 d x R = = d y d y 0 ; d z d z 0 (1.7) d t = R d t + e d x − v d t 0 1 0 0 r r If a pointlike structure moves with velocities u 0 and u relative to S0 and S, respectively, the velocity components are naturally given by = dx 0 = dy 0 = dz0 u0x ; u0y ; u0z dt0 dt0 dt0 = dx = dy = dz ux ; uy ; uz dt dt dt Dividing the first three equations (1.7) by the fourth one the transformations of velocities are obtained: u − v u = 0x x + − RR[] e1 u0x v (1.8) u0y u u = u = 0z y ; z R + e u − v R + e u − v 1 0x 1 0x For velocities parallel to the x axis eq.s (1.8) reduce to − = u0 v u (1.9) RR[] + e u − v 1 0 The transformations (1.1)-(1.5), and (1.7)-(1.9) contain only a free parameter, Superluminal signals and causality 511 e1 , the coefficient of x in the transformation of time, which can be fixed by choosing a clock synchronisation method. Different choices of e1 imply different theories of space and time which are empirically equivalent to a very large extent. Michelson type experiments, Doppler effect, aberration, occultations of Jupiter satellites, radar ranging of planets and elementary particle kinematics were shown to be insensitive to the choice of e1 [5]. = Accelerations modify the conceptual situation to the point that e1 0 becomes unavoidable [11]. Three cases have been investigated : 1. The accelerating spaceships. In the isotropic system S0 clocks have been synchronised with the Einstein method, by using light signals. Two identical spaceships A and B initially at rest on the x 0 axis of S0 have = internal clocks synchronised with those of S0 . At time t0 0 the spaceships start accelerating in the direction + x 0, and they do so in exactly the same way, so that they have the same velocity v (t0 ) at every time t0 of S0 . At = time t0 they reach a preestablished velocity v v(t0 ) and their acceleration ≥ ends. For t0 t0 the spaceships are at rest in a different inertial system S (which they concretely determine) in motion with velocity v with respect to S0 . The relationship between the coordinates of S0 and S is given by the = transformations (1) with e1 0 (not by the Lorentz transformations), because the delay between the times marked by clocks on board of A and B and those in S0 does not depend on position: since A and B had at every time exactly the same velocity, their clocks accumulated exactly the same delay with respect to S0 . Therefore two events simultaneous in S0 , taking place in points of space near which A and B are passing, must be simultaneous also for the travelers in A and B, and thus also in the rest system of the spaceships, S. This is clearly a situation of absolute simultaneity which cannot be accounted for if the Lorentz transformations are applied, but is = obtained from (1) with e1 0 (“inertial transformations”). Not only the absolute simultaneity arises spontaneously in S, but it provides the only reasonable description of the physical reality. To see this, suppose that in A and B there are two passengers who are homozygous twins. Naturally nothing can stop them from resynchronising their clocks, once the acceleration has ceased. However, if they do so, they discover to 512 F. Selleri have different biological ages at the same time of S, as they cannot resynchronise their bodies! Everything is regular, instead, if they do not modify the times shown by their clocks. 2. The rotating disk. The propagation of light along the rim of a circular rotating disk requires, in any reasonable theory, a velocity of light locally identical (in any point P on the rim) with the velocity of light relative to the inertial system instantaneously endowed with the same velocity as P. Unfortunately this condition is not satisfied in the standard relativistic approach. Given that all pssible points P are physically symmetrical, for the proof one needs only consider the velocity of light for a complete tour around the disk, with no reference to any synchronisation procedure. It has been shown that for calculating correctly, on the disk, the fundamental time delay between light pulses propagating in opposite directions around the disk, one = must use the velocity of light given by eq. (1.3) with e1 0 [12]. The same result allows one to explain the Sagnac effect which up to now received only unsatisfactory theoretical treatments [13]. In this way a clear improvement has been made over the relativistic theory which contains a discontinuity between the rims of slowly rotating large disks and the locally comoving inertial systems. 3. The gravitational potential of the sun. A longstanding problem of satellite physics is that all clocks in the earth centered inertial frame (including GPS satellite clocks) seem to be insensitive to the variations of the gravitational potential of the sun. A recent paper by Ron Hatch [14] has eliminated the puzzle by showing that on the earth orbit there is a precise equality between the consequences of the solar potential and those of the = extraterm needed to convert the transformations with e1 0 into the Lorentz transformations.
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